Ultrasound poroelastography is a cost-effective non-invasive imaging technique, which is able to reconstruct several mechanical parameters of cancer and normal tissue such as Young's modulus, Poisson's ratio, interstitial permeability and vascular permeability. To estimate the permeabilities, estimation of the strain time constant (TC) is required, which is a challenging task because of non-linearity of the exponential strain curve and noise present in the experimental data. Moreover, noise in many strain frames becomes very high because of motion artifacts from the sonographer, animal/patient and/or the environment. Therefore, using these frames in computation of strain TC can lead to inaccurate estimates of the mechanical parameters. In this letter, we introduce a cubic spline based interpolation method, which uses only the good frames (frame of high SNR) to reconstruct the information of the bad frames (frames of low SNR) and estimate the strain TC. We prove with finite element simulation that the proposed reconstruction method can improve the estimation accuracy of the strain TC by 46% in comparison to the estimates from noisy data, and 37% in comparison to the estimates from Kalman filtered data at an SNR of 30dB. Based on the high accuracy of the proposed method in estimating strain TC from poroelastography data, the proposed method can be preferred technique by the clinicians and researchers interested in non-invasive imaging of tissue mechanical parameters.